7/2x+4=2/x-1

Solution for 7/2x+4=2/x-1 equation:

7/2x+4=2/x-1

We move all terms to the left:

7/2x+4-(2/x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

7/2x-2/x+1+4=0

We calculate fractions


7x/2x^2+(-4x)/2x^2+1+4=0

We add all the numbers together, and all the variables

7x/2x^2+(-4x)/2x^2+5=0

We multiply all the terms by the denominator


7x+(-4x)+5*2x^2=0

Wy multiply elements

10x^2+7x+(-4x)=0

We get rid of parentheses

10x^2+7x-4x=0

We add all the numbers together, and all the variables

10x^2+3x=0

a = 10; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·10·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*10}=\frac{-6}{20}
=-3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*10}=\frac{0}{20}
=0
$